8 citations · 16 across the 13 of their papers we have counts for
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Arithmetical properties of real numbers related to beta-expansions
Hajime Kaneko
The main purpose of this paper is to study the arithmetical properties of values \(\sum_{m=0}^{\infty} β^{-w(m)}\), where \(β\) is a fixed Pisot or Salem number and \(w(m)\) (\(m=0…
On subwords in the base- expansion of polynomial and exponential functions
Hajime Kaneko, Thomas Stoll
Let be any word over the alphabet , and denote by either a polynomial of degree or for a fixed . Furthermore, denote by…
Corona limits of tilings : Periodic case
Shigeki Akiyama, Jonathan Caalim, Katsunobu Imai +1
We study the limit shape of successive coronas of a tiling, which models the growth of crystals. We define basic terminologies and discuss the existence and uniqueness of corona li…
Hensel's lemma for general continuous functions
Hajime Kaneko, Thomas Stoll
In the present paper, we generalize the well-known Hensel's lifting lemma to any continuous function . This answers a question posed by Ax…
On the digital representation of smooth numbers
Yann Bugeaud, Hajime Kaneko
Let be an integer. Among other results, we establish, in a quantitative form, that any sufficiently large integer which is not a multiple of cannot have simultaneousl…
Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers
Hajime Kaneko, Takao Komatsu
Recently, the Cauchy-Carlitz number was defined as the counterpart of the Bernoulli-Carlitz number. Both numbers can be expressed explicitly in terms of so-called Stirling-Carlitz…